Believe it or not, it is entirely possibly to hit the 5000 item limit that is put in place for any view of lists in SharePoint Online in Office 365. If you do hit this, you will find an error telling you that the item limit set by the administrator has been exceeded.
There is a limit of 5000 items in any view on a list - if your list is going to get anywhere near that limit, use an indexed column and then create filters that make sure that you won't go beyond 5000 items in a view. For example, limit a view to the last 12 months of data, or limit the view to 4000 items.
If you find yourself in the situation where you can't do anything with the list, having exceeded this 5000 item limit in the default view, you won't even be able to delete the list! If this happens, open the list in SharePoint Designer 2010, then click 'Administration Web Page' in the 'Manage' group on the ribbon. The ID is indexed by default, so create a view that is that is guaranteed to return less than 5000 items, using filtering based on the ID of the column. Now, go into that view and move out enough of the items in the list to get you below the 5000 item limit. Once that's done, you can create a new indexed column (or maybe more than one). Now, edit your views to filter based on those indexed columns. Good to go!
Again, prevention is better than cure here - It took me a few hours to find this work-around and you should always aim to reduce impact on users. After I first encountered this issue, I future-proofed using the tips above (indexing and view limits) to make sure that this wouldn't happen for other lists.
I hope this has helped a little bit. Drop a comment below if you have any questions or comments.